Let’s say we apply some kind of intervention to a sample, and then find that the mean of this sample is x̅_{I}(“*I*” for “intervention”). Could we use this to estimate the population parameters if *everyone* were to receive the same intervention?

We could guess that the new population mean, which we’ll call μ_{I}, would be somewhere around x̅_{I}. From the limited information we have, the sample mean is our best estimate for the new population mean. We call this a **point** **estimate** since it’s a single value rather than a range of values.

Actually, a range of values is exactly what we want. In this lesson, we’ll calculate **confidence intervals** for where μ_{I} might be; in other words, we’ll be fairly confident that μ_{I} is between two particular values. We’ll determine what these values should be.

In Lesson 6 you learned that for a normal distribution, most values (about 95%) are within two standard deviations of the mean.

We can extend this concept to sampling distributions: approximately 95% of sample means will fall within 2σ/√n of the population mean.

**This is a preview of Lesson 8. To access the full book, please purchase a hard copy or a digital version. If you opt for the digital version, you will receive a link via email within 1 business day.**

Continue to Lesson 9, or select a lesson below.

Lesson 1: Introduction to Statistical Research Methods

Lesson 2: Visualizing Data

Lesson 3: Central Tendency

Lesson 4: Variability

Lesson 5: Standardizing

Lesson 6: Normal Distribution

Lesson 7: Sampling Distributions

Lesson 8: Estimation

Lesson 9: Hypothesis Testing

Lesson 10: t-Tests for Dependent Samples

Lesson 11: t-Tests for Independent Samples

Lesson 12: Intro to One-Way ANOVA

Lesson 13: One-Way ANOVA: Test significance of differences

Lesson 14: Correlation

Lesson 15: Linear Regression

Lesson 16: Chi-Squared Tests

Afterward

Index